Question

A research company found that 11% of the people that they called agreed to participate in a survey.

If the company called 196 people, about how many would be expected to participate in the survey?

Answer 1

22 people would be expected to participate in the survey.

Explanation:

We are given that a research company found that 11% of the people that they called agreed to participate in a survey.

The company called 196 people and we have to find that how many would be expected to participate in the survey.

The above situation can be represented through binomial distribution;

`P(X=r)=\binom{n}{r} * p^(r)* (1-p)^(n-r); x = 0,1,2,3,.....`

where, n = number of trials (samples) taken = 196 people

r = number of success

p = probability of success which in our question is probability

that people agreed to participate in a survey, i.e; p = 11%

Let X = Number of people who agreed to participate in a survey

SO, X ~ Binom(n = 196, p = 0.11)

Now, the expected number of people who would participate in the survey is given by;

E(X) =
`n * p`

=
`196 * 0.11` = 21.56 ≈ 22 people

Hence, 22 people would be expected to participate in the survey.